Speaker
Prof.
Erik Aurell
(Computational Biology, KTH, Stockholm)
Description
I will consider the problem of minimized (expected)
dissipated work or released heat in systems described by
over-damped Langevin equation. The problem can be
mathematically stated as a standard stochastic optimization
problem, but turns out to have a suprisingly simple solution
in turns of Burgers equation (or nonlinear diffusion
equation) for an auxiliary field, and mass transport by the
corresponding velocity field [1].
One application of these results is an improvement of
Landauer's bound on the heat released when setting one bit,
if it has to be done in a finite time [2]. The refined bound
has the form of T log2 + K/t, where T log 2 is the Landauer
bound, t is the time of the process and K can be computed
from the initial and final states and an appropriate
solution of Burgers equation.
If temperature and/or the friction coefficient are not
constant in time and/or space a similar almost closed
formula can be derived, not from the released heat but for
the entropy production in the environment [3]. I will
discuss the conceptual issues we have encountered in this
direction.
[1] Erik Aurell, Carlos Mejia-Monasterio, Paolo
Muratore-Ginanneschi, Phys. Rev. Lett. 106, 250601 (2011)
[2] Erik Aurell, Krzysztof Gawȩdzki, Carlos
Mejía-Monasterio, Roya Mohayaee, Paolo Muratore-Ginanneschi
[arXiv:1201.3207]
[3] Stefano Bo, Erik Aurell, Antonio Celani and Ralf
Eichhorn (2012, in preparation).
